Is it necessary to bring vitamins and supplements in their original bottles?

No.

If you are referring to "pill" form, the answer is no.

I read a couple other threads on vitamins and medications, read the TSA site, but still unclear to me if I can bring them in my carry on or have to put them in checked luggage. If I carry them on, can I just leave them in my suitcase at screening or do I have to take them out and put them in the plastic basket along with my zip loc bag containing liquids. Also, can I bring a chocolate bar from home on? Thanks.

You can put them in your checked or carryon, TSA is not even going to check anything other than your liquids, shoes belt or underwire bra!